Gilera Runner very hard to start, stops when hot?

Hi,
I'm having trouble with my 1999 50CC Gilera Runner.
When cold, it's very difficult to start. Once running, it ticks over fine. When it has been running at higher revs as I'm riding, it stalls when I've come to a stop, unless I keep higher revs on it. Then when I open the throttle to pull off again, it 'bogs down' and cuts out, though it starts very easily when hot. I have to leave it for about 30 seconds untill I can rev it again without it cutting out. I've stripped the carb and given it a good clean, and that seems fine. There is an electronic choke, but I'm not sure if this is working (and I don't want to spend £50 on one 'just in case', is there an easy way to tell if the electric auto choke is working?) I've noticed that when it's being run with the throttle open on it's stand, there is a dark wet liquid coming out of the exhaust minifold. Could this indicate a problem?
So to recap my questions.
1) How can I check the electric auto choke?
2) Why could it be so difficult to start?
3) Why could it be cutting out after being revved with the throttle open?
4) Does the dark liquid around the exhaust minifold when being revved indicate anything?

All help/advice greatfully received.